SSE, the UK's second-largest energy provider, is to freeze gas and electricity prices for its 5 million customers until 2016, putting pressure on rivals to follow.

The company's price promise – which will last for at least 21 months – echoes Ed Miliband's call for a moratorium on energy price rises, which when made last September sparked outrage among industry and business leaders.

The pledge also came just ahead of the likely announcement of a full-scale competition investigation of the energy industry by the new Competition and Markets Authority.

The regulator Ofgem is expected to call in the CMA on Thursday, which would subject the big players to unprecedented scrutiny and could prompt calls for them to be broken up.

David Cameron, who last year dismissed Miliband's plan for a freeze as "unworkable" and "marxist", described the SSE price freeze as "hugely welcome".

He added that SSE had made clear that a principal factor allowing it to freeze prices was the government's decision to roll back green levies on energy bills, which saved households an average £50 a year.

The company is also axing 500 jobs and scaling back investment in windfarms as part of a cost-cutting plan and will split its wholesale and retail divisions in an effort to simplify its business.

SSE, which also trades as Scottish Hydro, Southern Electric, Swalec and Atlantic, was the first of the big six energy suppliers to raise fuel bills last autumn, with an 8.2% increase. That caused a political storm about high prices and soaring profits that led the government to partially lift the cost of green levies.

Alistair Phillips-Davies, SSE's chief executive, said he hoped people would see a company like his as part of the solution, not the problem. "We're setting out a positive agenda for customers, including our price freeze to 2016; we're making sure our own house is in order for the future by streamlining and simplifying our business; and we're making clear we wish to work with people to find more ways of taking costs out of energy bills."

Last year, Phillips-Davies complained that Miliband's proposed price freeze, which the Labour leader said would take effect if his party won next year's general election, would "lead to unsustainable loss-making retail businesses".

The managing director of SSE's retail arm, Will Morris, said the freeze would be unaffected by volatility in world wholesale energy prices, despite fears over the impact of Russia's confrontation with the west over Ukraine. He told Sky News: "Whatever President Putin does, our prices will not rise."

The company, which is expected to report a 9% increase in annual profits for the year that ends this month, expects its profit margin to fall from 5% to 2.5%.

Richard Lloyd, executive director of the consumer group Which?, welcomed the certainty the price freeze would bring to "hard-pressed" customers. "A bold move by SSE in an energy market badly in need of change," he wrote on Twitter.

Ann Robinson, director of consumer policy at uSwitch.com, said: "This is a U-turn to be applauded. SSE was the last supplier to pass on the government's levy cuts and reduce customer bills this winter – now they are the first to freeze prices until 2016. We welcome this commitment." In another echo of Labour policy, SSE announced it is carrying out a legal separation of its wholesale arm, which includes energy production and storage, from its retail division, which sells to homes and businesses. SSE also promised that staff would not face compulsory redundancies as it seeks to save £100m a year.

However, the company disappointed environmentalists by pulling out of an offshore windfarm off the Suffolk coast and halting investment in two further projects, one each off the Scottish and English coasts, until it has more confidence in the viability of the offshore industry.

The company, formerly known as Scottish and Southern Energy, said it was making arrangements to deal with the "uncertainty"over the Scottish independence referendum, while insisting it remained neutral on the outcome.

The energy secretary, Ed Davey, said SSE's price freeze pledge increased the pressure on other energy companies to do the same. "This will be welcome news for SSE's customers and shows that the government's work to reduce energy bills is working by lowering policy costs and driving competition. This shows that the big six are starting to realise they need to take big action if they want to keep their customers, who have been switching supplier in record numbers."

The big six – Centrica, SSE, RWE npower, E.ON, Scottish Energy and EDF Energy – control 95% of the market for retail supply.

"SSE have shown today that the big energy firms are able to cut their costs and profits, and be confident about their ability to weather potential uncertainty in the wholesale markets, to give bill payers long-term price security. Customers of the others will be asking whether their suppliers will do the same. The government encourages people to shop around for the best deal," Davey said.

Hot and cold

That was then ...

Last September Ed Miliband promised a 20-month energy price freeze if Labour won the general election. It prompted a hostile response.

SSE's Alistair Phillips-Davies said a freeze would "lead to unsustainable loss-making retail businesses".

Sir Roger Carr, then chairman of British Gas owner Centrica, warned that price controls would be "a recipe for economic ruin for a company".

Angela Knight, head of Energy UK, said freezing energy prices "will also freeze the money to build and renew power stations, freeze the jobs and livelihoods of the 600,000 plus people dependent on the energy industry and make the prospect of energy shortages a reality, pushing up the prices for everyone".

On Wednesday, SSE announced a price freeze to last at least until January 2016.

SSE's Alistair Phillips-Davies said: "We're setting out a positive agenda for customers, including our price freeze to 2016; we're streamlining and simplifying our business; and we wish to work with people to find more ways of taking costs out of energy bills. We're doing our bit ... we don't want to stop at 2016."

• This article was amended on 27 March 2014 to clarify that Sir Roger Carr is no longer chairman of Centrica. He was replaced by Rick Haythornthwaite this year.